Apollo Global Management has told time-share operator Hilton Grand Vacations it wants to buy the $2.4 billion outfit, and the company is considering its next steps, The Post has learned.

Apollo, co-run by Leon Black, gave the Orlando time-share company three options: It could buy Hilton Grand at a premium to its share price, merge the company with smaller Apollo-owned rival Diamond Resorts and keep the combined business public, or tender for Hilton Grand shares at a premium to the current Hilton Grand share price, sources said.

Apollo has not indicated what it would pay, but sources said the private equity firm could bid as much as $36 a share — a 28% premium over the company’s closing price Monday of $28.21 a share.

Hilton Grand on Aug. 1 reported disappointing earnings, and its shares are down more than 10% this month, giving suitors a chance to potentially buy it on a dip.

Apollo’s Black wants to combine Diamond Resorts, which it bought in September 2016, with Hilton Grand so it can cut costs and gain scale, sources said.

The CFO of Diamond, Jim Mikolaichik, was Hilton Grand’s CFO until last year.

Besides Apollo, the Blackstone Group could also be a suitor, sources said.

Hilton Worldwide Holdings, which Blackstone once controlled, spun off Hilton Grand in 2017. Blackstone then formed a joint venture with Hilton Grand to buy Elara, one of the world’s largest time-share resorts.

Blackstone President Jonathan Gray is still chair of Hilton Worldwide and licenses its name to Hilton Grand.

The time-share industry overall posted its ninth consecutive year of growth in 2018, according to the American Resort Development Association. Sales volume rose 7%, to $10.2 billion.

“The companies have a lot of control over demand,” giving them stable earnings, Jefferies’ David Katz said.

Typical customers include young families who want a predictable vacation home with multiple bedrooms and a kitchen, Katz said.